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Vectors and the Geometry of Space Three-Dimensional Coordinate SystemsVectorsThe Dot ProductThe Cross ProductLines and Planes in SpaceCylinders and Quadric Surfaces 13.
#THOMAS CALCULUS 11TH EDITION INTEGRATION FORMULAE SERIES#
Infinite Sequences and Series SequencesInfinite SeriesThe Integral TestComparison TestsThe Ratio and Root TestsAlternating Series, Absolute and Conditional ConvergencePower SeriesTaylor and Maclaurin SeriesConvergence of Taylor Series Error EstimatesApplications of Power SeriesFourier Series 12. Conic Sections and Polar Coordinates Conic Sections and Quadratic Equations Classifying Conic Sections by EccentricityQuadratic Equations and RotationsConics and Parametric Equations The CycloidPolar Coordinates Graphing in Polar CoordinatesArea and Lengths in Polar CoordinatesConic Sections in Polar Coordinates 11. Further Applications of Integration Slope Fields and Separable Differential EquationsFirst-Order Linear Differential EquationsEuler's MethodGraphical Solutions of Autonomous EquationsApplications of First-Order Differential Equations 10.
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Techniques of Integration Basic Integration FormulasIntegration by PartsIntegration of Rational Functions by Partial FractionsTrigonometric IntegralsTrigonometric SubstitutionsIntegral Tables and Computer Algebra SystemsNumerical IntegrationImproper Integrals 9. Transcendental Functions Inverse Functions and their DerivativesNatural LogarithmsThe Exponential Functionax and loga 圎xponential Growth and DecayRelative Rates of GrowthInverse Trigonometric FunctionsHyperbolic Functions 8. Applications of Definite Integrals Volumes by Slicing and Rotation About an AxisVolumes by Cylindrical ShellsLengths of Plane CurvesMoments and Centers of MassAreas of Surfaces of Revolution and The Theorems of PappusWorkFluid Pressures and Forces 7. Integration Estimating with Finite SumsSigma Notation and Limits of Finite SumsThe Definite IntegralThe Fundamental Theorem of CalculusIndefinite Integrals and the Substitution RuleSubstitution and Area Between Curves 6. Applications of Derivatives Extreme Values of FunctionsThe Mean Value TheoremMonotonic Functions and the First Derivative TestConcavity and Curve SketchingApplied Optimization ProblemsIndeterminate Forms and L'Hopital's RuleNewton's MethodAntiderivatives 5. Differentiation The Derivative as a FunctionDifferentiation RulesThe Derivative as a Rate of ChangeDerivatives of Trigonometric FunctionsThe Chain Rule and Parametric EquationsImplicit DifferentiationRelated RatesLinearization and Differentials 4. Limits and Derivatives Rates of Change and LimitsCalculating Limits Using the Limit LawsPrecise Definition of a LimitOne-Sided Limits and Limits at InfinityInfinite Limits and Vertical AsymptotesContinuityTangents and Derivatives 3. (Practice Exercises, Additional Exercises, and Questions to Guide Your Review appear at the end of each chapter.) Preliminaries Real Numbers and the Real LineLines, Circles, and ParabolasFunctions and Their GraphsIdentifying Functions Mathematical ModelsCombining Functions Shifting and Scaling GraphsTrigonometric FunctionsGraphing with Calculators and Computers 2. Giordano.ġ volume (various pagings) : illustrations (some color) 26 cm